In science, living matter is an oft-used term referring to matter that is alive or in possession of the properties of life. The term is often used in the context of life thermodynamics. The following 1993 quote by American chemist Martin Goldstein gives one example: [1]

“To apply thermodynamics to the problem of how life got started, we must ask what net energy and entropy changes would have been is simple chemical substances, present when the earth was young, were converted into living matter [as in the formation of a mouse] … to answer this question [for each process], we must determine the energies and entropies of everything in the initial state and final state.”

History
The term "living matter" seems to date back to at least the 17th century. In 1908, English physiologist David Harris defined living matter to be a type of matter or bioplasm in possession of the property whereby if it receives a stimulus it will respond in some way or another to the stimulus. [2] In the early part of the 20th century, before the rise of chemical thermodynamics in the 1920s, terms such as “vital energy” or “biotic energy” were used to describe the energy transformations in living matter. [3] Towards the turn the 20th century the term seems to have fallen in to marginal disuse, possibly superseded by terms such as living organism, living system, living structure, or living being.

References
1. Goldstein, Martin and Goldstein, Inge F. (1993). The Refrigerator and the Universe: Understanding the Laws of Energy (section: Entropy of a mouse, pgs. 297-99). Harvard University Press.
2. Harris, David F. (1908). The Functional Inertia of Living Matter: a Contribution to the Physiological Theory of Life (pg. 1). J. & A. Churchill.
3. Moore, Benjamin. (1921). Biochemistry: a Study of the Origin, Reactions, and Equilibria of Living Matter (term: biotic energy, pgs. 1, 17-18, etc.; term: vital energy, pg. 128). Longmans, Green & Co.

Further reading
● Stephens, Charles A. (1888). Living Matter: Its Cycle of Growth and Decline in Animal Organisms. The Laboratory Co.
● Loeb, Jacques. (1906). The Dynamics of Living Matter. Columbia University Press.
● Krebs, H.A. and Kornberg, H.L. (1957). Energy Transformations in Living Matter. Springer-Verlag.